Predictable zone for phase-resolved reconstruction and forecast of irregular waves

• Published in: Wave motion Vol. 77; pp. 195 - 213
• Main Authors: Qi, Yusheng, Wu, Guangyu, Liu, Yuming, Yue, Dick K.P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.2018; Elsevier BV
• Subjects: Gravitational waves; Gravity waves; Phase-resolved wave prediction; Predictions; Reconstruction; Relativity; Set theory; Studies; Wave predictability; Wave propagation; Wave reconstruction; Phase-resolved wave prediction; Wave predictability; Wave reconstruction; Wave propagation; Gravity waves
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2017.12.001

Our interest is the phase-resolved reconstruction and forecast of multidirectional irregular gravity wave fields based on specific wave measurements. We consider the theoretical predictable zone P in space–time within which the phase-resolved wave field can be fully reconstructed/forecasted based on the given measurements. Using linearized wave theory and reasonable assumptions of the frequency and directional extent of the wave field, we obtain closed-form expressions for P in terms of set theory expressions involving the individual measurement. We derive and illustrate P obtained for measurements at one or more fixed locations over time, for moving probes, for whole-area wave measurements, and combinations of these. We also consider the problem of optimal deployment of these measurements to maximize the volume of P in space–time. For J probes under optimal deployment, we show that the volume of P relative to that of a single probe scales as J3 for large J. •Phase-resolved predictable zone of irregular waves for given measurements is derived.•The predictable zone is derived in closed-form expression based on linearized wave theory.•Measurements can be one or more fixed/moving probes and/or whole-area measurements.•Optimal deployment of measurements to maximize the predictable zone is derived.•Asymptotic estimate of predictable zone volume for large number of measurements is obtained.